Lattice calculation of medium effects at short and long distances

The perturbative description of the Quark-Gluon Plasma (QGP) breaks down even at very high temperatures [1]. The reason for this is the generation of different length (time) scales at finite temperature. At high temperatures (T ≫ ΛQCD) the gauge coupling constant is small g ≪ 1 and well separated length scales exist: 1/T ≪ 1/(gT ) ≪ 1/(gT ). For such high temperatures the region of applicability of the perturbation theory is established. While for distances smaller than 1/T the ordinary perturbation theory should be applicable, at distances smaller than 1/gT the hard thermal loop resummed perturbation theory [2] should be applied. For distances larger than 1/gT , however, perturbation theory is no longer valid [1]. For interesting temperatures up to a few times Tc, however, g>∼1 and it is not clear up to which distances (times) the perturbation theory is applicable. At short distances r ≪ T one expects that medium effects are not important. For such small distances one should also expect the ordinary perturbation theory to be viable, because at zero temperature perturbation theory works at short distances. Naturally the question arises: at what distances the medium effects become important and up to which distance perturbation theory is applicable? In the present work we try to answer these questions by studying the heavy quark potential and temporal quark and gluon propagators in Coulomb gauge.